Simplify the following expression: $\dfrac{32p}{28p^5}$ You can assume $p \neq 0$.
Answer: $ \dfrac{32p}{28p^5} = \dfrac{32}{28} \cdot \dfrac{p}{p^5} $ To simplify $\frac{32}{28}$ , find the greatest common factor (GCD) of $32$ and $28$ $32 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $28 = 2 \cdot 2 \cdot 7$ $ \mbox{GCD}(32, 28) = 2 \cdot 2 = 4 $ $ \dfrac{32}{28} \cdot \dfrac{p}{p^5} = \dfrac{4 \cdot 8}{4 \cdot 7} \cdot \dfrac{p}{p^5} $ $\phantom{ \dfrac{32}{28} \cdot \dfrac{1}{5}} = \dfrac{8}{7} \cdot \dfrac{p}{p^5} $ $ \dfrac{p}{p^5} = \dfrac{p}{p \cdot p \cdot p \cdot p \cdot p} = \dfrac{1}{p^4} $ $ \dfrac{8}{7} \cdot \dfrac{1}{p^4} = \dfrac{8}{7p^4} $